In prior-art transfer devices, the transfer between longitudinal and cross conveyors in the form of chain, twin-belt, single-belt or roller conveyors takes place by means of rotary tables, which pick up the individually packaged product or the carrier for the individually packaged product, such as a container or pallet, when the rotary table is stopped and slowly pivot it about the center of the individually packaged product or along an arc into the release direction of the second conveying section in order to release the individually packaged product there. Curved pieces are also known in roller conveyors, which themselves have cylindrical cross rollers and a lateral guide. The rollers are driven in order to support a change in direction of the individually packaged product in the curve. The change in direction is brought about preferably by the lateral guide, which prevents the individually packaged product from running off the curved path.